Actually, for a smaller 4X DSD file, if I put 352 KHz in the >768 line, I get a 352 KHz file. And putting 176 KHz there produces a 176 KHz file. I am not sure why it is different for what you are seeing. I am using 25.0.108. I have always thought that putting all the sample rates up to 4xDSD into Output Format would be a good idea. But, fortunately, you can usually get it to work as is.
I believe the factor of 8 conversion is arbitrary. The original author decided to, loosely, turn 8 0s and 1s into a PCM number. He could have decided to use 16 instead of 8. I do not know the whole history, but there was one public source set of code to do this that many people used originally. A 2.822 MHz file turns into a 352 KHz PCM file, which gives people plenty of room to decide how they want to resample the PCM to the final sample sample.
One more thing to consider is the filter that has to be applied after a DSD to PCM conversions. Due to the nature of DSD, with a PCM conversion, there is ever increasing noise at higher frequencies. It should not be allowed into the electronics. In original SACD, Sony used a 48 dB/octave filter low pass filter at 50 KHz. That is a steep enough filter to remove the noise. The JRiver default for that filter is 48 dB/octave at 24 Khz. There are also options for 24 dB/octave at 30 Khz and 50 KHz. The default is very effective, but quite conservative in terms of frequency. The higher frequency ones are, unfortunately, not quite step enough to really eliminate the noise. You can turn the filters off and set your own Sony like filter (48 dB/octave at 50 KHz) in DSP Studio Parametric Equalizer, although I do not know the quality of the filter. The standard filter options are in Tools - Audio - Advanced - Input Plugins - DSD. You can also increase the sound level by +6dB in that section, if desired. Some people do, but it runs the risk of clipping on occasions.